Prove the following statements about flows in a network.
(a) Prove that if f is a flow in a network (N,s,t,c), then for all s - t cuts (X,Xˉ) in (N,s,t,c), v(f)=f(X, Xˉ)−f( Xˉ ,X).
(b) Prove that if f is a flow in a network (N,s,t,c), then for all s - t cuts (X,Xˉ) in (N,s,t,c), v(f)≤c(X, Xˉ).